Abstract
The robustness of complex networks is of great significance. Great achievements have been made in robustness optimization based on single measures, however, such networks may still be vulnerable to multiple attack scenarios. Therefore, recently, multi-objective robustness optimization of networks has received increasing attention. Nevertheless, several challenges remain to be addressed, including the different computational complexities in evaluating the objectives, insufficient diversity in the obtained networks, and high computational costs of the search process. In this paper, we address the aforementioned challenges by developing a computationally efficient multi-objective optimization algorithm. Based on the unique features of complex networks, a new parallel fitness evaluation method guided by a network property parameter is designed, and embedded in a reference vector guided multi-objective evolutionary algorithm. In addition, a surrogate ensemble with heterogeneous inputs is constructed based on graph embedding information to efficiently estimate multiple robustness of networks. The proposed algorithm is validated on synthetic and real-world network data and our results show that the designed algorithm outperforms the state-of-the-art method with a marked improvement on the computational efficiency. Compared with other single-objective optimization methods, the proposed algorithm demonstrates a considerable exploitation ability.